618 CHAPTER 6 The Circular Functions and Their Graphs Find the linear speed v for each of the following. 109. the tip of the minute hand of a clock, if the hand is 7 cm long 110. the tip of the second hand of a clock, if the hand is 28 mm long 111. a point on the edge of a flywheel of radius 2 m, rotating 42 times per min 112. a point on the tread of a tire of radius 18 cm, rotating 35 times per min 113. the tip of a propeller 3 m long, rotating 500 times per min (Hint: r = 1.5 m) 114. a point on the edge of a gyroscope of radius 83 cm, rotating 680 times per min 115. a point on the equator moving due to Earth’s rotation, if the radius is 3960 mi 116. a person on a Ferris wheel with radius 50 ft, revolving twice per minute Solve each problem. See Examples 5 and 6. 117. Speed of a Bicycle The tires of a bicycle have radius 13.0 in. and are turning at the rate of 215 revolutions per min. See the figure. How fast is the bicycle traveling in miles per hour? (Hint: 5280 ft = 1 mi) 13.0 in. 118. Hours in a Martian Day Mars rotates on its axis at the rate of about 0.2552 radian per hr. Approximately how many hours are in a Martian day (or sol)? (Data from The World Almanac and Book of Facts.) 119. Angular and Linear Speeds of Earth The orbit of Earth about the sun is almost circular. Assume that the orbit is a circle with radius 93,000,000 mi. Its angular and linear speeds are used in designing solar-power facilities. 93,000,000 mi Sun Earth u NOT TO SCALE (a) Assume that a year is 365 days, and find the angle formed by Earth’s movement in one day. (b) Give the angular speed in radians per hour. (c) Find the approximate linear speed of Earth in miles per hour. 120. Angular and Linear Speeds of Earth Earth revolves on its axis once every 24 hr. Assuming that Earth’s radius is 6400 km, find the following. (a) angular speed of Earth in radians per hour (b) linear speed at the North Pole or South Pole (c) approximate linear speed at Quito, Ecuador, a city on the equator (d) approximate linear speed at Salem, Oregon (halfway from the equator to the North Pole)
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